Question

in an atwood machine what would be value of tension and acceleration when body a is thrice massive as a body​

Answer 1

Given:

In an Atwood machine, given that body a is thrice massive as body b.

To Find:

What would be value of tension and acceleration?

Solution:

Since, it is given that-  body a is thrice massive as body b.

therefore, let mass of body b = m2= m

and mass of body a = m1= 3(m2)=3m

Also, we know that-

Tension of Atwood machine is given by,

$T=\dfrac{2g \ m1m2}{m1+m2}$

on putting values, we get

$T=\dfrac{2g \ (3m)(m)}{3m+m} \\\\ =\dfrac{6g \ m^2}{4m} \\\\ =\dfrac{3}{2} \ mg$

Hence, tension is 3/2 mg.

Also, acceleration on an Atwood machine is given by;

$a=g\dfrac{m1-m2}{m1+m2}$

on putting values,  we get

$a=g\dfrac{3m-m}{3m+m} \\\\ =g\dfrac{2m}{4m}\\\\ =\dfrac{1}{2} g$

Hence, acceleration of Atwood machine is 1/2 g.